In the plane rectangular coordinate system, the standard equation of a circle with point O(a, b) as the center and radius R is (x-a) 2+(y-b) 2 = r 2.

Especially, the standard equation of a circle with the origin as the center and the radius r(r0) is x 2+y 2 = r 2.

General equation of circle:

The equation x 2+y 2+dx+ey+f = 0 can be transformed into (x+d/2) 2+(y+e/2) 2 = (d 2+e 2-4f)/4. Therefore:

(1), when d 2+e 2-4f0, the equation represents a circle with (-D/2, -E/2) as the center and (d 2+e 2-4f)/2 as the radius;

(2) When d 2+e 2-4f = 0, the equation represents a point (-D/2,-e/2);

(3) When d 2+e 2-4f0, the equation does not represent any graph.

Parametric equation of a circle:

The parametric equation of a circle with point O(a, b) as the center and R as the radius is x=a+r*cos, y=b+r*sin, where is the parameter.

Endpoint formula of circle: If two points A (A 1, B 1) and B (A2, B2) are known, the equation of circle with line segment AB as its diameter is (X-A1) (X-A2)+(Y-B1) (Y

The eccentricity of a circle is e=0, and the radius of curvature of any point on the circle is r.

The tangent equation of a point M(a0, b0) on a circle x 2+y 2 = r 2 is A0 * x+B0 * y = r 2.

A point M(a0, b0) outside the circle (X 2+Y 2 = R 2) leads to two tangents of the circle, which are A and B, so the equation of the straight line where the two points A and B are located is A0 * X+B0 * Y = R 2.

Equation of circle:

1. Definition of a circle: The set of points whose distance to a point on a plane is equal to a fixed length is called a circle, the fixed point is the center of the circle, and the fixed length is the radius of the circle.

2. Equation of circle

(1) standard equation, center and radius r;

(2) General equation

At that time, the equation represented a circle. At this point, the center is and the radius is.

At that time, I said a point; At that time, the equation did not represent any graph.

(3) Method of solving cyclic equation:

Generally, the undetermined coefficient method is adopted: first set, then seek. Determining a circle requires three independent conditions. If the standard equation of a circle is used,

Demand a, b, r; If you use general equations, you need to find d, e, f;

In addition, we should pay more attention to the geometric properties of the circle: for example, the vertical line of a chord must pass through the origin, so as to determine the position of the center of the circle.

3, the position relationship between straight line and circle:

The positional relationship between a straight line and a circle can be divided into three situations: separation, tangency and intersection:

(1) Set a straight line and a circle, and the distance from the center of the circle to L is, then there is; ;

(2) Tangent to a point outside the circle: ①k does not exist, verify ②k exists, establish an oblique equation, and solve k with the distance from the center of the circle to the straight line = radius to get the equation.

(3) The tangent equation of the point passing through the circle: if the circle (x-a) 2+(y-b) 2 = R2 and a point on the circle is (x0, y0), then the tangent equation passing through the point is (x0-a) (x-a)+(y0-b) (y-b) =

4. The positional relationship between circles: it is determined by comparing the sum (difference) of the radii of two circles with the distance (d) between the center of the circle.

Set a circle,

The positional relationship between two circles is usually determined by comparing the sum (difference) of the radii of the two circles with the distance (d) between the center of the circle.

At that time, the two circles were separated, and there were four common tangents at this time;

At that time, the two circles were circumscribed, and the connection line crossed the tangent point, with two outer tangents and one inner common tangent;

At that time, the two circles intersect, and the connecting line bisects the common chord vertically, and there are two external tangents;

At that time, two circles were inscribed, and the connecting line passed through the tangent point, and there was only one common tangent;

At that time, two circles included; It was concentric circles.

Note: when two points on the circle are known, the center of the circle must be on the vertical line in the middle; It is known that two circles are tangent and two centers are tangent to the tangent point.

The auxiliary line of a circle generally connects the center of the circle with the tangent or the midpoint of the chord of the center of the circle.

How to preview mathematics;

Read the upcoming math content before class, so as to have a clear idea, so as to grasp the initiative in class. This is conducive to improving learning ability and forming the habit of self-study, so it is an important part of mathematics learning.

Read and write. (No pen and ink, no reading)

(1) Reading, thinking and writing are generally used to draw out or mark the main points, levels and connections of the content, write down your own opinions or mark the places and problems that you don't understand;

(2) Once you find that you don't master the old knowledge well or even understand it, you should turn over the books in time and take measures to make up for it, so as to create conditions for learning new content smoothly.

(3) Understand the basic content of this lesson, that is, know what to talk about, what problems to solve, what methods to adopt, where the key points are, and so on.

Take out the chapters corresponding to a workbook and read them roughly to see which questions can be read at once and which questions can't be understood at all, and then go to class with questions.

The concept of numbers:

One number is the fraction of another number, generally referring to the ratio: standard labor should be found in the production group, compared with each other and evaluated as a number.

A number that indicates that one number is a fraction of another number is called a number.

Usually used in industrial and agricultural production, indicating the increase of output. A few percent is a few tenths.

For example, grain output increased by "20%".

"20%" means two tenths, which means that the grain output has increased by 20%.

When calculating a number, there are two numbers, A and B. Find the ratio of B and A and turn the ratio into a pure decimal. Then the pure decimal is called the number from B to A. The first digit after the decimal point is called "Cheng" or "Minute", and the second digit after the decimal point is called "Li".

For example, if the planned grain output is 50,000 Jin and the actual grain output is 1 10,000 Jin, then the grain yield increase percentage is 1.275 = 0.2, that is, the grain yield is increased by 20%.

Mutual transformation between several numbers and other numbers;

Methods: The score X 10= Chengdu/10= decimal (Chengdu divided by 10 equals decimal) and Chengdu X 10= percentage.